The two countries are separated by a body of water known as the Taiwan Strait. The Taiwan Strait ranges in width from 80 to 125 miles.

When relations between China and the US go up and down like a yo-yo, it is usually because of an argument the two countries have over Taiwan.

The argument is over the amount of contact the US has with Taiwan. China would sooner have the US deal only with China and not with Taiwan. Here is why Taiwan is such a sore point with China.

Although it represents only 18 million people, Taiwan considers itself the real China. China, or mainland China as it is sometimes called to avoid confusion, says that's nonsense. Its argument is that there can be only one China and that it is the real China representing a country of about 1 billion people. It sees Taiwan as a province of mainland China, not something that stands apart as a separate country.

The confusion all started in 1949 because of a civil war on mainland China. A civil war is a war fought not against a foreign country but between two sides within the same country. An example of this was the American Civil War, when the North and the South fought.

In the case of China, it was between the Nationalists and the Communists. The Communists were so successful that in 1949 they were strong enough to form their own government. That government, which still rules today in Peking, the capital of China, is known as the People's Republic of China. A lot of people call it Communist China for short.

Meanwhile, 2 million Nationalists who had lost the war fled to the nearby island of Taiwan and set up their own noncommunist government, which they call the Republic of China. They hold onto the name of China because they still believe they represent all the people of China. Some day they hope to go back and get control of mainland China again. At first, most governments in the world said that the Chinese government they would recognize was the government of Taiwan, based in the capital city of Taipei.

But over a period of time more and more governments began to think it made no sense not to recognize mainland China when it represented about a quarter of the world's population. So, bit by bit, these governments stopped recognizing - that is, stopped accepting officially - Taiwan as the true government of China. Instead, they began to recognize mainland China as the only government of the Chinese people.

The world community as a whole agreed with the switch when a resolution was passed at the United Nations General Assembly on Oct. 25, 1971. This resolution expelled the Republic of China (Taiwan), and gave UN membership, including a seat on the UN Security Council, to the People's Republic of China (mainland or Communist China).

The vote was 76 countries in favor; 35 against (including the US) and 17 countries that abstained. Abstained means remained neutral. The countries voted neither for nor against the resolution.

The United States had hoped there could be two Chinas in the world. But neither of the two Chinas wanted another China. Each insisted it was the only China.

Ten years ago, in February 1972, US President Richard M. Nixon visited Peking , the capital of the People's Republic of China. He said that the US now recognized Taiwan as a part of mainland China. It was a terrible shock for the Chinese on Taiwan, who felt that the US had switched sides. They felt betrayed.

At the time of President Nixon's stay in China, a statement came out which left no doubt about the new US position. It said: ''The US acknowledges that all Chinese on either side of the Taiwan Strait maintain that there is but one China and that Taiwan is part of China. The United States government does not challenge that position.'' It also said the question of Taiwan should be left to the Chinese people themselves.

The US didn't officially recognize China, though, until seven years later - on Jan. 1, 1979. Also the US didn't cut itself off completely from Taiwan. There are still trade and cultural links. Most important of all, the US still supplies Taiwan with arms. That is why there is a fuss about those fighter aircraft.

The aircraft are so advanced that China feels Taiwan could use them against it. What worries China the most, though, is that by supplying these aircraft the US is continuing links with Taiwan and treating it, in effect, as an independent country.

China doesn't mind Taiwan having its own government and army, but it wants Taiwan to be part of mainland China and not act on its own.